solving the vehicle routing problem with simultaneous pickup and delivery by an effective ant colony optimization

one of the most important extensions of the capacitated vehicle routing problem (cvrp) is the vehicle routing problem with simultaneous pickup and delivery (vrpspd) where customers require simultaneous delivery and pick-up service. in this paper, we propose an effective ant colony optimization (eaco) which includes insert, swap and 2-opt moves for solving vrpspd that is different with common ant colony optimization (aco). aco is a meta-heuristic algorithm inspired by the foraging behavior of real ants. artificial ants are used to build a solution for the problem by using the pheromone information from previously generated solutions. an extensive numerical experiment is performed on 68 benchmark problem instances involving up to 200 customers available in the literature. the computational result shows that eaco not only presented a very satisfying scalability, but also was competitive with other meta-heuristic algorithms such as tabu search, large neighborhood search, particle swarm optimization and genetic algorithm for solving vrpspd problems.